Surrey Police said a man had been arrested on suspicion of murder and attempted murder after the incident in Ashford, Surrey, on Thursday.
The woman was pronounced dead at the scene, and the child has been taken to hospital where she remains, police confirmed.
Neighbours living near an apartment block in Woodthorpe Road called Imtech House said they heard “screaming and shouting” before police arrived and the scene turned into “chaos”.
They told the PA news agency: “It was chaos. We heard screaming and shouting. It was definitely a woman. Ashford is a peaceful area but that block is problematic. It’s a great shame.”
Another said: “I saw a child being taken out and a man being arrested. There was a very large police presence and an air ambulance.”
One resident claimed his friend lived in the housing block and he was shut out of his flat for three hours while police attended.
He added: “There was an air ambulance that landed at a field in the nearby primary school. There are a lot of really lovely people living in there, but they’re vulnerable.”
Police said they attended a property at 1.15pm on Thursday following a report of concern for safety.
The victims and the man arrested, who is in his 30s, were known to each other, and there is not believed to be any wider risk to the community, the force said.
Senior investigating officer detective chief inspector Kimball Edey, of Surrey Police, said: “This investigation is in its early stages and a team of specialist officers are working around the clock to gather as much information as possible.
“Our thoughts are with the family and friends of the victims at this unbelievably difficult time.”
Nearly 400 people have previously signed a petition “demanding that Spelthorne Council tackles antisocial behaviour connected to Imtech House”.
